Maximum margin multiclass nearest neighbors

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17 Scopus citations

Abstract

We develop a general framework for margin- based multicategory classification in metric spaces. The basic work-horse is a margin- regularized version of the nearest-neighbor classifier. We prove generalization bounds that match the state of the art in sample size n and significantly improve the dependence on the number of classes κ. Our point of departure is a nearly Bayes-optimal finite-sample risk bound independent of κ. Although κ-free, this bound is un- regularized and non-adaptive, which motivates our main result: Rademacher and scale-sensitive margin bounds with a logarithmic dependence on κ. As the best previous risk estimates in this setting were of order √κ, our bound is exponentially sharper. From the algorithmic standpoint, in doubling metric spaces our classifier may be trained on n examples in CJ(n2 log n) time and evaluated on new points in 0(log n) time.

Original languageEnglish
Title of host publication31st International Conference on Machine Learning, ICML 2014
PublisherInternational Machine Learning Society (IMLS)
Pages2501-2511
Number of pages11
ISBN (Electronic)9781634393973
StatePublished - 1 Jan 2014
Event31st International Conference on Machine Learning, ICML 2014 - Beijing, China
Duration: 21 Jun 201426 Jun 2014

Publication series

Name31st International Conference on Machine Learning, ICML 2014
Volume3

Conference

Conference31st International Conference on Machine Learning, ICML 2014
Country/TerritoryChina
CityBeijing
Period21/06/1426/06/14

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